A tightly wound San Antonio police officer is charged with protecting a witness in the trial of the head of a drug cartel in Hot Pursuit, a movie which probably at some point sounded like a good idea.

I can kind of see it: the straight-man straight arrow lady cop trying to rein in the diva-ish Latin trophy wife. Also, both the actresses playing them are — by Hollywood standards — older; Reese Witherspoon is 39 and Sofia Vergara is almost 43, which also offers some smart comedy possibilities. There could be some subverting of stereotypes, some goofiness, some sly social commentary.

Could be. Isn’t.

Rose Cooper (Witherspoon) grew up revering her police officer father and went into the force herself. But she’s been stuck in the evidence room since accidentally tasing (and briefly setting fire to) a civilian who called “shotgun,” referring to a car ride and not a weapon. She gets her chance to get back in the field when the U.S. Marshals ask her to help transport and protect witnesses heading to a big trial in Dallas. Rules require a female officer for a female witness, so while the male marshal watches her husband, Daniella Riva (Vergara) will be looked after by Rose.

Almost immediately, things go wrong. First, a pair of masked gunmen show up and shoot Riva’s husband and the U.S. Marshal. Then, another pair of masked gunmen show up. The rivaling gunmen shoot at each other and at Cooper as she tries to find and rescue Riva, who is hiding in her car. Cooper jumps into the driver’s seat and heads out, with both sets of gunmen presumably after them.

At first, Cooper is relieved when a pair of officers from her precinct comes to her aid, but she recognizes the tattoo on one of the men’s wrists and soon she realizes that she is being chased not only by, probably, the drug kingpin’s men but also by dirty cops. She’s not surprised when she learns that she and Riva have been declared fugitives. Nevertheless, Cooper is determined to get Riva to Dallas for the trial — the only way, she thinks, to clear their names and keep them from being murdered.

If you took 2013’s The Heat (which starred Sandra Bullock and Melissa McCarthy as the rules-obsessed FBI agent and street-savvy Boston cop, respectively) and made it badly, the result would have been something like Hot Pursuit. Like The Heat, Hot Pursuit is a female buddy comedy built on opposite types. But The Heat took the basic neat cop/messy cop framework and did all sorts of fun things with it. The women were actually both examples of professional competence and both had healthy egos and strange quirks.

Hot Pursuit never really goes beyond its outline. Witherspoon is an older variation on her Tracy Flick character but with absolutely no layers or dimensions. Vergara is her Modern Family Gloria character but with a harder edge. Cooper is short, Riva is tall. Cooper always seems to be in uniform, even when she’s out of uniform; Riva is a girlier girl. They are on the run, they grudgingly gain a respect for each other. There is no part of their partnership or friendship or the course of the story that you couldn’t guess. And all of the comedy comes from the most surface, unimaginative places: the different ways the two women talk (Cooper is all cop jargon, Riva’s heavily accented Spanglish is played for laughs), their physical differences and the moments of physical comedy that suggest girl-on-girl action. Oh, tee-hee, they are pretending to kiss! It all feels very mid-1990s sitcom. Very third-tier mid-1990s sitcom, like the summer replacement for the 9:30 p.m. Thursday night show on NBC that is still losing to reruns on other networks.

About halfway through the movie, a love interest for Cooper is jammed sideways into the plot. The character, named Randy, brings nothing to the movie, but it is entertaining to watch the British actor white-knuckle his Texan accent. British + Texan in this case equals something that frequently sounded Australian to me.

Way back in its most zygote form, Hot Pursuit might have had the possibility to be something interesting or at least funny. But what little potential it might have had was squashed by layers upon layers of lazy choices. C-

Rated PG-13 for sexual content, violence, language and some drug material. Directed by Anne Fletcher and written by David Feeney & John Quaintance, Hot Pursuit is an hour and 27 minutes long and is distributed by Warner Brothers.